1. Let X1, Xn be i.i.d. random variables with a pdf .... f(x) = = e-(x-0), 10, x > 0, elsewhere for a constant parameter 0. This pdf is called the shifted exponential. (a) Compute the c.d.f. of Y = min(X1, ..., Xn). and investigate the distribution that Yn converges in distribution. (b) Compute the c.d.f. of Zn = n(Y₁-0). Investigate the distribution that Zn converges in distribution.

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A: f(x)=3x2; 0&lt;x&lt;1

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A: Given: The cumulative distribution function is as follows F(x) = x3     0&lt; x &lt; 1

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A: Step 1:Step 2:Step 3:Step 4:Option(E) : correct

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A: Here, Beta(2,3) F(x) = 6x^2 - 8x^3 + 3x^4

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A: The cumulative distribution function is defined as F(x) = P(X ≤ x)

Q: 17. Let (y1, Y2, ..., Yn) be a random sample from a normal distribution such that E(y;) = a + Bxi,…

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A: The moment generating function(MGF) for a random variable is given by MXt=EetX where E denotes…

Q: (1) Let X = b(16,) find E(4-3x) and distribution function.

A: From the provided information, X~b (16, 1/4) Sample size (n) = 16 Probability (p) = 1/4

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Q: (1) Let X b(16, find E(4-3x) and distribution function.

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Q: Question is attached.

A: Given thatThe moment generating function of a random variable isTo find mean and variance:

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A: Note: Hi, thank you for the question. As per our company guideline we are supposed to answer only…

Q: 5. Let X be a random variable with the PDF f(x) = r - 1| for 0 0.5) (c) Calculate E(X) and Var(X)

A: The pdf of X is

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A: Probability density Function -        fxx of the random variable X is define as :-…

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